A note on saturated distinguished chains of length one

Let (K,v) be a Henselian valued field. In this paper, we investigate algebraic elements ?? having saturated distinguished chains of length one over K. We provide some characterizations for them. In particular, we characterize all irreducible polynomials over K whose roots have saturated distinguished chains of length one. Moreover, using the properties of such elements we give various necessary, sufficient, or both conditions for the metric invariants of algebraic elements to be equal.